Sums of Powers of Integers

Summary: This paper generalizes the well-known fact that "the sum of the first \(n\) positive cubes is the square of the sum of the first \(n\) positive numbers." The generalization examines any polynomial relationship between "the sum of the first \(n\) positive \(j\) th powers" and "the sum of the first \(n\) positive \(k\)th powers" for any \(j\) and \(k\).